Gas Turbine Engine Fan Blade FlutterDetection Using Casing Vibration Signalsby Application of Recurrence Plotsand Recurrence Quantification Analysis

A. N. Viswanatha Rao, V. P. S. Naidu, and Soumendu Jana

Abstract Gas turbine aero engines are a specific class of turbomachinery whereincompression system and turbine are realized as spinning discs on an interconnectingshaft. Fan-bladed disc undergoes an unsteady aeroelastic phenomenon known asflutter during various operational regimes, which might lead to structural failure ofblades. Study of this mode of flutter induced structural response by measuring casingvibration is of interest in health monitoring of aero engines. In this paper, authorspresent a novel application of detecting the rotating blade flutter based on the featurespace constructed using statistical parameters, recurrence plots (RP) and recurrencequantification analysis (RQA) of engine casing vibration data. Feature vectors thusobtained are visualised in several 3D vector space plots to cluster the data pointswhich separate flutter mode from the normal mode of operation. Results obtainedthrough the proposed method have been compared with engine flutter test resultsobtained through dedicated rotating blade strain gauge instrumentation.

Keywords Flutter · Recurrence plots · Bladed disc · Casing vibration ·Low-pressure compressor (LPC) · High-pressure compressor (HPC)

A. N. Viswanatha Rao (B) · V. P. S. Naidu · S. JanaAcademy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, Indiae-mail: vishwanatha@gtre.drdo.in

V. P. S. Naidue-mail: vpsnaidu@nal.res.in

S. Janae-mail: sjana@nal.res.in

A. N. Viswanatha RaoDRDO—Gas Turbine Research Establishment, Bengaluru 560093, India

V. P. S. Naidu · S. JanaCSIR—National Aerospace Laboratories (NAL), Bengaluru 560017, India

© Springer Nature Singapore Pte Ltd. 2021J. S. Rao et al. (eds.), Proceedings of the 6th National Symposiumon Rotor Dynamics, Lecture Notes in Mechanical Engineering,https://doi.org/10.1007/978-981-15-5701-9_31

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Nomenclature

1F First flexural mode2F Second flexural mode1T First torsional modeNL LPC spool speedNH HPC spool speedRPS Revolutions per secondEO Engine ordersksp/s Killo samples per second

1 Introduction

Gas turbine engine-based propulsion system of an aircraft is one of the flight safetycritical systems, which encompass various disciplines of science and technology. Adevelopmental aero engine under consideration is an augmented low bypass ratiotwin spool turbofan with a dry thrust rating of 51 kN and maximum after burnerthrust of 81 kN. The engine has been configured with an axial flow fan of threestages and six stages of core compressor. It has an annular combustor, single-stagecooled high-pressure turbine operating at maximum temperature of 1700 K and asingle-stage unshrouded low-pressure turbine [1].

In order to meet the requirements of high thrust to weight ratio (>7), aero enginestructures are designed to operate with lower factor of safety margins. Cyclic loadexperienced during vibration of engine components leads to fatigue failure. Enginerotating blades get excited by aerodynamic instabilities like rotating stall, surge andby aeroelastic instability termed as flutter [2].

Bladed disc assemblies experience system level vibratory modes referred to asnodal diameters. Generally, at any particular rotational speed of engine, if a resonantcondition of blades exists, then such a crossovermay lead to high cycle fatigue failure.The Campbell diagram graphically represents such resonance crossover condition ofblades. It is a 2D plot, where in measured or predicted natural frequencies of bladesand corresponding excitation by engine rotational speed are presented. Blades canvibrate in flexural modes 1F and 2F and torsional modes 1T. While in operation,excitation by rotor at harmonics of the rotational speed can also excite the vibration,and these excitation lines are termed 2EO, 3EO, 4EO and so on [2]. There areseveral sources of excitation during engine operation, which can lead to vibrationof blades. A case study of aeroelastic flutter in a transonic axial compressor rotorbased on analytical methods has been discussed in. The unsteady airflow that leadsto aerodynamic force fluctuation close to fan blade natural frequency, resulting inexcitation of the blades, has been discussed at length. A study of the structural anddynamic behaviour of bladed disc assembly is crucial to decide whether the responseis due to flutter or not [3].

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Structural health monitoring of the engine is of paramount importance duringdevelopmental tests. Hence, in order to monitor the blade vibration and flutterphenomenon, extensive instrumentations are carried out during developmental tests.Engine test data obtained during development phase forms the basis for life andusage monitoring algorithms, which would be used during subsequent operationalphase. One of the critical healthmonitoring instrumentations that would be employedduring operational phase of the engine is the casing vibration [4]. In this paper, dataanalysis algorithm of detecting flutter signatures from the casing mounted vibrationsensor has been developed and validated with known cases of flutter. Gas turbineengines used for aircraft propulsion application must meet safety and reliabilityrequirements. High degree of reliability is achieved by suitable design and propermaintenance schedules. When any fault is reported by the monitoring instrumenta-tion, detailed fault diagnosis is undertaken which is complex and time-consuming.In order to aid the fault diagnosis, statistical methods that rely on feature extractiontechnique have evolved over the past two decades [5].

2 Flutter in Fan of a Gas Turbine Engine

The fan of a gas turbine engine under consideration is shown in Fig. 1a. In thisconfiguration, fan blades are assembled on to the disc through a dovetail interface toform a bladed disc assembly as shown in Fig. 1b. Due to the complex geometry andtwist of fan blades, the aerodynamic load, centrifugal forces acting during rotationresult in blades experiencing both bending and torsion motions. First stage of thefan-bladed disc assembly is of particular interest since this is the highly loaded stage,which handles the entire mass flow into the engine, and is having the longest blades,which vibrate with high amplitude and at relatively low frequency.

Flutter is a self-induced vibration due to instability in the bladed disc system inany turbomachinery and is usually associated with one of the blade’s fundamental

Fig. 1 a Third-stage axial fan of a gas turbine engine. b First-stage fan rotor blade disc

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modes (bending or torsion) with a frequency close to the natural frequency. Duringflutter, condition aerodynamic forces induced due to blade vibration feed energyback into the bladed disc structure itself. This leads to stress pile-up in each cycleof vibration and can result in structural damage. One noticeable feature of flutterinduced vibration is that it is non-integral to the engine rotational speed [6, 7].

3 Instrumentation to Acquire Flutter Signals

Engine is instrumented extensively during developmental tests with a suitable dataacquisition system to obtain high-quality aerodynamic performance data for the fanmodule under tests. Transient dynamic data from strain gauges, casing flush-mountedhigh-frequency response pressure transducers and casing vibration are acquired withwide bandwidth data acquisition systems. Rotational speed of the engine is a funda-mental parameter for blade health monitoring. Blade vibrationmeasurement requiresa reference signal, which is essentially a once-per-revolution (1/rev) signal from fan-bladed disc. It is an eddy current sensor, which senses the passing of a referencefeature on the low-pressure compressor shaft. This signal gives an angular referencepoint on the spool, which would be useful for identifying the exact blade in therotating disc [8].

Engine casing structural vibration level on the fan casing is measured by a piezo-electric accelerometer (CA 134/5 of Vibrometer©, USA make). The sensor has awide dynamic range of measurement up to 500 g and sensitivity of 10pc/g and abandwidth of 6 kHz. The bandwidth requirements for casing vibration are ~2 kHzwhich can sense tenth harmonic of LPC spool speed and eighth harmonic of theHPC spool speed when engine is tested 10–100% speed. In addition to the vibration,casing flush-mounted miniature piezo-resistive pressure sensors (XT-190-25G) areused for detecting unsteady aerodynamic phenomena like rotating stall, surge andflutter [8].

3.1 Rotor Blade Vibration

Traditionally, blade vibration is measured using strain gauges during initial phasesof engine development. Strain gauge measures strains experienced by rotor blades.During the experimental evaluation of the fan, foil-type strain gauges of karma© (74Ni, 20 Cr, 3 Al, 3 Fe) with a gauge factor of 2 were used. These are small in size, lowin mass, easy to attach to fan blade through an adhesive [9]. Gauges are placed onspecific locations based on finite element studies to capture various modes of bladevibration [10]. Lead wires from the strain gauges are routed through the blade rootdovetail to the rotating slip ring/telemetry system to transfer the data from rotatingsystem to the static frame as shown in Fig. 2.

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Fig. 2 a Fan rotor blade strain gauge. b Fan rotor blade strain gauge and rotating instrumentationarrangement. Courtesy GTRE

In order to evaluate the presence of flutter in the fan, elaborate testing procedure isrequired. It is established both analytically and experimentally that fan blade flutteroccurs at a defined corrected rotational speed [2]. During engine test at the normallyaspirated test cell, speed is gradually increased, while carefully watching the build-up of flutter signals simultaneously through strain signals from blades and casingmounted vibration sensors. Upon appearance of flutter signals, engine is acceleratedaway from the flutter speed band. Since strain gauge measurement is in rotatingframe of reference, the sensors would pick up the strain response of the blades assingle tone signature when blades vibrate. The Campbell diagrams shown in Fig. 3a,b indicates marginal strain build-up at 2EO crossover and flutter occurring at 1.8EOasynchronously.

Fig. 3 a Campbell diagram of the fan blades (theoretical estimates). b Non-sychronous (1.8 EO)blade response shown flutter in fan blades (Experimental results)

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4 Casing Vibration Signals

Rotation of the engine is the excitation for any vibratory response of engine subsys-tems. Hence, it is an industry practice to analyse the vibratory response by usingthe concept of engine order tracked RMS levels. It can be seen from Fig. 4a thatwhen the engine fan speed crosses the flutter speed band, RMS level of the casing

Fig. 4 aEngine casingvibrationRMSvalue trend analysis andb spectrogramof the casingvibrationon fan

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vibration increases. Such a response is due to pressure wave prevailing inside theengine during flutter which acts on the inner surface of the engine casing forcing itto respond by casing vibration. During this state of the engine, the spectrogram ofthe casing vibration shown in Fig. 4b has several frequency components as definedin Ref. [6]. During flutter, one or more circumferential travelling pressure waves setin, each with a specific nodal diameter as described in Ref. [7]. It has been shownby analysis in ref [7] that the frequency of the signals sensed by the casing mountedsensors is given by Eq. 1, in a stationery frame of reference can be computed asfollows:

f s = f b + nNL (1)

where

f s frequency sensed by a casing mounted sensor in Hzf b frequency of vibrating blade in Hzn 1, 2, 3, 4…,f frequency in Hz andNL Rotational speed in RPS.

5 Flutter Analysis Frame Work

Initially, data analysis was carried out on four engine tests by conventional time–frequency methods using well-established analysis algorithms provided DATSframework by PROSIG© [11] which conclusively identified the existence of flutterof the fan blades based on the theoretical Campbell diagram 3(a) and experimentalresults shown in Fig. 3b. Further an exploratory analysis was taken up on casingvibration data patches extracted at instances 1 and 2 as shown in Fig. 4a. Test casesof flutter-free operation of fan as well as flutter condition were analysed as per theanalysis framework shown in Fig. 5.

Fig. 5 Flow chart of the fan flutter signal analysis framework

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6 Recurrence

Recurrence is an inherent property of any dynamical processes in nature. Manydynamic phenomena in complex systems, natural or engineered, have these twopatterns, i.e. (1) recurrence wherein a set of states occur and repeat often and (2) thetrajectory of states, which evolve, follows a specific pattern. In a dynamical system,there are a set of states betweenwhich it dwells often.Byobserving a few significantlycontributing patterns in a time domain signal, it is possible to determine the tendencyof a system towards a particular state [12]. Recurrence-based analysis method hasemerged as powerful tool for visualization as recurrence plots (RP) and analysis ofcomplex dynamical systems. Further, the quantification of recurrence that has led to anew analysis tool called recurrence quantification analysis (RQA), which is effectiveto detect transitions in the dynamics of systems from a time series data. This methodhas been demonstrated to work effectively even with one-dimensional (1D) timeseries data [13]. However, there are not much research publications on usage of RPfor diagnosis of gas turbine engine faults. In this research work, recurrence plotsand associated analysis have been carried out on vibration data from casing mountedsensors during flutter as described in Fig. 5.

6.1 Phase Space

Sampled data obtained by a sensing system is a time series, which describes thechanges of the systems over a period. This data is transformed to the phase space byuse of time delay approach based on the Takens’ embedding theorem [14] in givenby Eq. 2:

X (1) = {x(1), x(1+ τ ), x(1+ 2τ ), x(1+ 3τ ), . . . , x(1+ (m − 1)τ ), x(1+ mτ )}X (2) = {x(2), x(2+ τ ), x(2+ 2τ ), x(2+ 3τ ), . . . , x(2+ (m − 1)τ ), x(2+ mτ )}X (3) = {x(3), x(3+ τ ), x(3+ 2τ ), x(3+ 3τ ), . . . , x(3+ (m − 1)τ ), x(3+ mτ )}

::X (i) = {x(i), x(i + τ ), x(i + 2τ ), x(i + 3τ ), . . . , x(i + (m − 1)τ ), x(i + mτ )} (2)

where X is a state vector of dimension m; x is the instantaneous data; i = 1, 2, 3, …,N; m is the dimension parameter; τ is the delay parameter.

For the analysis of time series, the parameters, i.e. embedding dimension m andthe delay time τ have to be chosen appropriately.

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6.2 Recurrence Plot (RP)

In the study of recurrences in dynamical systems, recurrence plot was constructedbased on phase space. It is a technique to visualize the behaviour of m-dimensionalphase space trajectories. It is a graphical representation of such points in time, whenthe trajectory recurs in a ε-neighbourhood to a former state. The state of a system atith instance of time, and at another instance of time j is depicted in a two-dimensionalplot of black andwhite spots, where black spot marks repeated occurrence. Here bothX- and Y-axes are the time as shown in Fig. 7.

A recurrence instance can be mathematically given in Eq. 3:

Ri, j (ε) = !(ε||xi − x j ||), i, j = 1, Z , (3)

where Z is the number of considered states xi, ε is a threshold distance, ||.|| is a normand!(·) the Heaviside function. A comprehensive discussion on the recurrence plotsand their interpretation is described in Ref. [14].

6.3 Recurrence Quantification Analysis (RQA)

The recurrence quantification analysis (RQA) is a process of data analysis wherequantification of the number and duration of recurrences of a dynamical system arepresented by its state space trajectory. Small cluster of points, such as diagonal lines,horizontal and vertical lines, random points in the recurrence plots are used to quanti-tatively describe recurrence plots and arrived at the framework of quantification. TheRQA method has been enhanced since inception by introduction of several quan-tification measures such as determinism (DET), recurrence rate (RR), laminarity(LAM), RP entropy (RP-ENT), length of diagonal lines (RP-Lmax), trapping time(TT). Details on the RQA are available in Ref. [14].

6.4 Recurrence Analysis of Casing Vibration Data

As the name suggests, the recurrence plot is a pictorial representation of repeatedoccurrence of a state in a system.When engine is operating normally, as the fan bladesrotate at a constant angular velocity, each blade passes over a reference point as arepeating phenomenon. A cyclic phenomenon of bladed disc rotation coupled withvibrating blades, i.e. repetition of few cycles of blade vibration while completingone rotation of the disc, needs to be captured by the RP. It may be recalled thatblades vibrate due to resonance when engine speed and natural frequency of bladescross over. Design guidelines itself ensure that selection and placement of any twoadjacent blades on the fan disc to be slightly apart in order not to have all blades

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getting excited together. However, during flutter mode of excitation, all blades ofthe fan disc go into a single frequency of vibration close to its natural frequency. Byexploiting this unique feature of blade vibration during flutter, recurrence plots canbe constructed effectively.

In order to identify the possible flutter crossover band, RMS value of the casingvibration was considered to identify the speed band (82–89% of NL) where suddenincrease in casing vibration RMS level is shown in Fig. 4a. During most of the tests,engine speed was scheduled for crossover at a ramp rate of 20 rpm/s which lastedfor a duration of ~40 s from 70 to 90% of power setting. This mode of operationwas essential to avoid pile-up of blade strain levels which could lead to failure ofthe blades and also to get confirmed flutter data. During most of the engine tests,flutter band crossover occurs four times, i.e. two acceleration and two decelerations.Data was sampled at 8.823 ksp/s. Since engine speed is continuously accelerating ordecelerating throughout the flutter data capture duration, it is essential to have a quasi-steady condition for the RP to be effectively obtained. Each revolution during fluttercrossover is about 7 ms (time for one rotation around flutter speed ~145 ± 3 Hz), andeach blade would be passing across the vibration sensor at time interval of 0.291 ms(7/24). By the prior knowledge, the flutter frequency at 1F mode is ~290 ± 5 Hz,and the frequency of the signal felt by the stationary frame of reference would be570–590 Hz (1F + 2NL). When engine casing vibrates during flutter, accelerometermounted on the casingwould sense the harmonics of flutter signal. Since the vibrationsignal has several other frequency components, it is essential to capture the frequencyof interest.

In order to effectively capture recurrence feature in a signal, embedding dimensionm and delay parameter τ need to be iteratively and intuitively varied to arrive at anoptimumcombination.Aparametric studywas carried out by constructing recurrenceplots with delay parameter τ varied from 1 to 100 and embedding parameter fixedat 3. Observations made on the phase space trajectories during this study are shownin Table 1.

Autocorrelation of the signal was carried out in order to get an explanation forobservations made in Table 1. When engine is operating in flutter-free speed band(NL speed in the range 149–151 RPS), the correlation peaks in a repetitive manneronce in 58 samples are shown in Fig. 6a. Inter-sample gap of 58 gives a time periodof ~6.6 ms (1/8823 * 58) which is the time taken for one rotation of LPC spool(NL = 149 RPS). Further, autocorrelation study of signals during flutter speed band(NL ~ 142–148 RPS) shows a cyclic peaking pattern every 7.5 samples as shown inFig. 6b. It can be inferred from the autocorrelation results that when the embeddingparameter τ = 15 (which is 2 times 7.5) gives a time period of ~1.7 ms (15 * 1/8823)which corresponds to the flutter frequency band 588 ± 1 Hz (which is 292 Hz + 2X148 Hz, i.e. 1F + 2NL) observed in a stationary frame of reference. Methodologyof constructing recurrence plots requires to set the delay parameter τ which is theindex of the data array to an integer number only. Since the embedding dimensionm is 3, it is essential to have three data samples which are separated by the delayparameter τ within contiguous 15 samples. Based on the constraints as discussed, τ

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Table 1 Parametric study to arrive at optimal value of τ

Dimensionparameter m

Delayparameter τ

Phase space image Observations Remarks

3 15, 30, 45, 60,75, 90

Cylindricalimage

τ set at exactlyat the fluttersignaturefrequency basedonautocorrelation

3 1 to 100excluding 15,30, 45, 60, 75,90

Toroid image τ not set awayfrom the fluttersignaturefrequency basedonautocorrelation

3 1–100 SphericalImage

No flutter. Whenτ is in the range52–53, theimage takes theshape of a toroid

(a) )b(rettulferofeB During flutter

Fig. 6 Autocorrelation of the casing vibration

is optimally arrived at 5 which gives the phase space vector the data with indices asn + 1, n + 6 and n + 11 where n = 1, 2, 3, 4, till end of data array.

Two windows of data just before occurrence of flutter and during flutter are takenfor analysis. The window size is optimally fixed at 13,000 samples, which amountsto about 200 revolutions of engine test where the assumption of quasi-steady stateof the engine can be made with fair degree of certainty. During each window ofdata, 13 contiguous sets of 1000 samples are extracted as pages for the RPs. DuringRP construction with casing vibration data, embedding dimension of 3 and delayparameter of 5 were decided based on the parametric study carried out as describedearlier. The delay parameter of 5 gives a clear evolution of the phase space into anellipsoid-shaped image as can be seen in Fig. 7a–f.

It can be seen from the phase space, colour RP and binary RP that there aresignificant features in the images which differentiate the flutter condition from thenormal operation. Such 52 plots were constructed for each engine test which hastwo crossovers. After a careful visualization study, in order to aid an automated

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(a) Phase space before onsert of flutter

(b) Colour RP before onset of flutter

(c) Binary RP before onset of flutter

(d) Phase space during flutter (e) Colour RP dur ing flutter (f) Binary RP during flutter

Fig. 7 Phase space, colour RP and binary RP for flutter crossover

decision-making process, RP images were processed by the RQA which extractseveral features as described. These features vectors are extracted from each RP.Totally, 104 engine test data points were processed to demonstrate the efficacy of theRP-based flutter analysis. Among the 104 data sets, 52 data sets are taken just priorto flutter excitation and 52 data sets are during flutter mode of blade vibration.

6.5 Results of Recurrence Quantification Analysis

Among all the RQA parameters, three parameters RR, DET and Lmax were found tohave noticeable variations between the presence and absence of flutter. In order tovisualize the RQA features, a 3D feature space was constructed as shown in Fig. 8.Even though there is a clear clustering of data points separating flutter region fromnormal region, a distinct clustering of RQA features was not being emerged, andthere were few out layers.

6.6 Statistical Analysis of Vibration Signal During Flutter

In addition to the RQA features, general statistical features such as mean, variance,RMS, skewness, kurtosis and entropy for the data were also analysed for the casingvibration signals during flutter test of fan. These statistical features are analysed

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(a) Engine test #1 for Flutter Evaluation (b) Engine test #2 for Flutter Evaluation

Fig. 8 Clustering of RQA features

Fig. 9 Statistical features to distinguish between presence and absence of flutter

for their sensitivity and clustering, i.e. their ability to classify the flutter state of theengine from normal state. A 3D feature space of statistical features was created usingselected feature vectors, which exhibited noticeable variations. It is clear from Fig. 9that the feature vectors of selected statistical features in the 3D scatter plot show agood separation between flutter condition and otherwise with few outliners.

6.7 Feature Vector Fusion

In order to improve the clustering of flutter condition data points, a fusion of RQAfeatures and statistical features was taken up for a study. Two 3D scatter plots wereconstructed with kurtosis, variance and RQA-Lmax as a one feature vector as shownin Fig. 10a and RQA-Lmax, variance and kurtosis as the other feature vector as shownin Fig. 10b. It can be seen that there is a clear demarcation of data points, whichseparate presence and absence of flutter condition.

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Fig. 10 a Fusion of variance, kurtosis andRQA-Lmax.bFusion ofRQA-DET, variance and kurtosis

7 Conclusions and Future Work

In order to avoid premature failure of rotor blades due to fatigue caused by flutterinduced vibration, a framework of online monitoring and offline analysis is essential.Such a framework essentially would be an interdisciplinary analysis methodologyof structural and aerodynamic phenomenon. Engine test engineers are generallyconstrained by limited instrumentation, lack of validated monitoring methodologiesduring initial developmental engine tests. Under such circumstances, analysis basedon statistical methods, feature recognition and multi-sensor data fusion enhance thedecision-making process of the test engineers. An engine-monitoring framework,which has been discussed in this paper, helps in decision making whether flutterexists or not with fair degree of certainty based on casing vibration data alone. Theanalysis needs a small data slice acquired during test and a general analysis algo-rithm, which can be implemented easily for online monitoring. Upon detection offlutter signatures online, detailed investigation can be taken up with a comprehen-sive rotating instrumentation to sense and quantify resulting blade deformation andprevailing aerodynamic conditions dedicated instrumentation. The parametric studyconducted on selecting delay parameter τ has revealed unique phase space images.There is a need to explore this further and extract features on these geometric imagesas a measure of flutter magnitude. Usage of RP can be extended to cross RP whereinthe phase space can be constructed from twoor three identical sensors located circum-ferentially around the engine casing to fuse multi-sensor data towards enhancing theconfidence level.

Acknowledgements The authors are thankful to the director, Gas Turbine Research Establishment(GTRE), Bangalore, and National Aerospace Laboratories (NAL), Bangalore, who has given anopportunity to take up this research work. They also thank Mr. Vikas, scientist, working in theinstrumentation and control engineering group of GTRE for helping in various data analysis work.

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